Could you please try to find the intersections points of this two functions: $ y = x $ and $y=(a+x) \ {\rm e}^ {-2(a+x)} $ with $x\geq0$
Thanks for your help
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Sign up to join this communityCould you please try to find the intersections points of this two functions: $ y = x $ and $y=(a+x) \ {\rm e}^ {-2(a+x)} $ with $x\geq0$
Thanks for your help
To visualize the pairs of real numbers {x, a}
that satisfy the equation,
you can use ContourPlot
:
ContourPlot[(a + x) E^(-2 (a + x)) == x, {x, -2, 1}, {a, 0, 5}]
or RegionPlot
with options MeshFunctions
+ Mesh
:
RegionPlot[True, {x, -2, 1}, {a, 0, 5},
BoundaryStyle -> None,
MeshFunctions -> {(#2 + #) E^(-2 (#2 + #)) - # &},
Mesh -> {{0}},
MeshStyle -> Directive[Thick, Red],
PlotStyle -> None,
PlotPoints -> 100]
Looks like you'll need some constraints on a
.
a = -1;
f[x_] := (a + x) E^(-2 (a + x))
Plot[{x, f[x]}, {x, 0.001, 4}, PlotRange -> {Automatic, {-2, 1}}]